Socialization is the process by which kids learn the values of the culture in which they live. Kids are socialized first by their parents and then later by friends and teachers. In many societies, the different genders are expected to behave quite differently -- this is a value in such societies. So gender socialization is the process by which a kid is taught how his or her gender is "supposed to" behave.
For example, a child might be taught that "boys don't cry" or that girls don't play rough games. These sorts of socialization play a large role in setting up gender stereotypes and attitudes that persist later in life.